Free: Contests & Raffles.
That table shows cottontail is classified as game animals. I don't see how they can legally be taken with air guns...
I don't believe it matters if cotton tails are native. They are listed in the regs as a game animal and have a season, therefore they can only be shot by a licensed hunter with legal weapons. Sounds like they were released in the 1930's to be a game animal and that is what they are now even if they weren't native originally.